The second order formalism of Hartle is used to study
slowly and rigidly rotating stars with focus on the quadrupole
moment of the object. The second order field equations for the
interior fluid are solved numerically for different classes of
possible equations of state and these solutions are then matched to
a vacuum solution that includes the general asymptotically flat
axisymmetric metric to second order, using the Darmois-Israel
procedure. For these solutions we find that the quadrupole moment
differs from that of the Kerr metric, as has also been found for
some equations of state in other studies. Further we consider the
post-Minkowskian limit analytically. It is also illustrated how
the relativistic multipole moments can be calculated
from a complex gravitational potential.
